i need to know how to implement solid wall and far-field boundary conditions for van leer flux vector splitting scheme, if anyone is aware or can guide me to some reference.

hi: assuming you mean (VAN) LEER; one way of implementing the boundary conditions is by introducing (GHOST CELLS): that is; you generate in your code a group of cells that are taged as ghost cells. Having this done; you should put a (SUITABLE) values of the primitive variables ( rho, u, ...) such that the boundary conditions are satisfied ( in your case [solid wall = no slip] condition ).

The same applies for the far field BCs. The simpliest far field BCs are identified through the method of characteristics (either you copy them from the flow field or simply impose the infinity values ; this depends on the characteristics). If you wish to implement more complicated far field boundary conditions find some thing about the so called "sponge layer".

good luck!